kpeter@814: /* -*- C++ -*-
kpeter@814:  *
kpeter@814:  * This file is a part of LEMON, a generic C++ optimization library
kpeter@814:  *
kpeter@814:  * Copyright (C) 2003-2008
kpeter@814:  * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
kpeter@814:  * (Egervary Research Group on Combinatorial Optimization, EGRES).
kpeter@814:  *
kpeter@814:  * Permission to use, modify and distribute this software is granted
kpeter@814:  * provided that this copyright notice appears in all copies. For
kpeter@814:  * precise terms see the accompanying LICENSE file.
kpeter@814:  *
kpeter@814:  * This software is provided "AS IS" with no warranty of any kind,
kpeter@814:  * express or implied, and with no claim as to its suitability for any
kpeter@814:  * purpose.
kpeter@814:  *
kpeter@814:  */
kpeter@814: 
kpeter@814: #ifndef LEMON_CYCLE_CANCELING_H
kpeter@814: #define LEMON_CYCLE_CANCELING_H
kpeter@814: 
kpeter@814: /// \ingroup min_cost_flow
kpeter@814: ///
kpeter@814: /// \file
kpeter@814: /// \brief Cycle-canceling algorithm for finding a minimum cost flow.
kpeter@814: 
kpeter@814: #include <vector>
kpeter@814: #include <lemon/adaptors.h>
kpeter@814: #include <lemon/path.h>
kpeter@814: 
kpeter@814: #include <lemon/circulation.h>
kpeter@814: #include <lemon/bellman_ford.h>
kpeter@814: #include <lemon/howard.h>
kpeter@814: 
kpeter@814: namespace lemon {
kpeter@814: 
kpeter@814:   /// \addtogroup min_cost_flow
kpeter@814:   /// @{
kpeter@814: 
kpeter@814:   /// \brief Implementation of a cycle-canceling algorithm for
kpeter@814:   /// finding a minimum cost flow.
kpeter@814:   ///
kpeter@814:   /// \ref CycleCanceling implements a cycle-canceling algorithm for
kpeter@814:   /// finding a minimum cost flow.
kpeter@814:   ///
kpeter@814:   /// \tparam Digraph The digraph type the algorithm runs on.
kpeter@814:   /// \tparam LowerMap The type of the lower bound map.
kpeter@814:   /// \tparam CapacityMap The type of the capacity (upper bound) map.
kpeter@814:   /// \tparam CostMap The type of the cost (length) map.
kpeter@814:   /// \tparam SupplyMap The type of the supply map.
kpeter@814:   ///
kpeter@814:   /// \warning
kpeter@814:   /// - Arc capacities and costs should be \e non-negative \e integers.
kpeter@814:   /// - Supply values should be \e signed \e integers.
kpeter@814:   /// - The value types of the maps should be convertible to each other.
kpeter@814:   /// - \c CostMap::Value must be signed type.
kpeter@814:   ///
kpeter@814:   /// \note By default the \ref BellmanFord "Bellman-Ford" algorithm is
kpeter@814:   /// used for negative cycle detection with limited iteration number.
kpeter@814:   /// However \ref CycleCanceling also provides the "Minimum Mean
kpeter@814:   /// Cycle-Canceling" algorithm, which is \e strongly \e polynomial,
kpeter@814:   /// but rather slower in practice.
kpeter@814:   /// To use this version of the algorithm, call \ref run() with \c true
kpeter@814:   /// parameter.
kpeter@814:   ///
kpeter@814:   /// \author Peter Kovacs
kpeter@814:   template < typename Digraph,
kpeter@814:              typename LowerMap = typename Digraph::template ArcMap<int>,
kpeter@814:              typename CapacityMap = typename Digraph::template ArcMap<int>,
kpeter@814:              typename CostMap = typename Digraph::template ArcMap<int>,
kpeter@814:              typename SupplyMap = typename Digraph::template NodeMap<int> >
kpeter@814:   class CycleCanceling
kpeter@814:   {
kpeter@814:     TEMPLATE_DIGRAPH_TYPEDEFS(Digraph);
kpeter@814: 
kpeter@814:     typedef typename CapacityMap::Value Capacity;
kpeter@814:     typedef typename CostMap::Value Cost;
kpeter@814:     typedef typename SupplyMap::Value Supply;
kpeter@814:     typedef typename Digraph::template ArcMap<Capacity> CapacityArcMap;
kpeter@814:     typedef typename Digraph::template NodeMap<Supply> SupplyNodeMap;
kpeter@814: 
kpeter@814:     typedef ResidualDigraph< const Digraph,
kpeter@814:       CapacityArcMap, CapacityArcMap > ResDigraph;
kpeter@814:     typedef typename ResDigraph::Node ResNode;
kpeter@814:     typedef typename ResDigraph::NodeIt ResNodeIt;
kpeter@814:     typedef typename ResDigraph::Arc ResArc;
kpeter@814:     typedef typename ResDigraph::ArcIt ResArcIt;
kpeter@814: 
kpeter@814:   public:
kpeter@814: 
kpeter@814:     /// The type of the flow map.
kpeter@814:     typedef typename Digraph::template ArcMap<Capacity> FlowMap;
kpeter@814:     /// The type of the potential map.
kpeter@814:     typedef typename Digraph::template NodeMap<Cost> PotentialMap;
kpeter@814: 
kpeter@814:   private:
kpeter@814: 
kpeter@814:     /// \brief Map adaptor class for handling residual arc costs.
kpeter@814:     ///
kpeter@814:     /// Map adaptor class for handling residual arc costs.
kpeter@814:     class ResidualCostMap : public MapBase<ResArc, Cost>
kpeter@814:     {
kpeter@814:     private:
kpeter@814: 
kpeter@814:       const CostMap &_cost_map;
kpeter@814: 
kpeter@814:     public:
kpeter@814: 
kpeter@814:       ///\e
kpeter@814:       ResidualCostMap(const CostMap &cost_map) : _cost_map(cost_map) {}
kpeter@814: 
kpeter@814:       ///\e
kpeter@814:       Cost operator[](const ResArc &e) const {
kpeter@814:         return ResDigraph::forward(e) ? _cost_map[e] : -_cost_map[e];
kpeter@814:       }
kpeter@814: 
kpeter@814:     }; //class ResidualCostMap
kpeter@814: 
kpeter@814:   private:
kpeter@814: 
kpeter@814:     // The maximum number of iterations for the first execution of the
kpeter@814:     // Bellman-Ford algorithm. It should be at least 2.
kpeter@814:     static const int BF_FIRST_LIMIT  = 2;
kpeter@814:     // The iteration limit for the Bellman-Ford algorithm is multiplied
kpeter@814:     // by BF_LIMIT_FACTOR/100 in every round.
kpeter@814:     static const int BF_LIMIT_FACTOR = 150;
kpeter@814: 
kpeter@814:   private:
kpeter@814: 
kpeter@814:     // The digraph the algorithm runs on
kpeter@814:     const Digraph &_graph;
kpeter@814:     // The original lower bound map
kpeter@814:     const LowerMap *_lower;
kpeter@814:     // The modified capacity map
kpeter@814:     CapacityArcMap _capacity;
kpeter@814:     // The original cost map
kpeter@814:     const CostMap &_cost;
kpeter@814:     // The modified supply map
kpeter@814:     SupplyNodeMap _supply;
kpeter@814:     bool _valid_supply;
kpeter@814: 
kpeter@814:     // Arc map of the current flow
kpeter@814:     FlowMap *_flow;
kpeter@814:     bool _local_flow;
kpeter@814:     // Node map of the current potentials
kpeter@814:     PotentialMap *_potential;
kpeter@814:     bool _local_potential;
kpeter@814: 
kpeter@814:     // The residual digraph
kpeter@814:     ResDigraph *_res_graph;
kpeter@814:     // The residual cost map
kpeter@814:     ResidualCostMap _res_cost;
kpeter@814: 
kpeter@814:   public:
kpeter@814: 
kpeter@814:     /// \brief General constructor (with lower bounds).
kpeter@814:     ///
kpeter@814:     /// General constructor (with lower bounds).
kpeter@814:     ///
kpeter@814:     /// \param digraph The digraph the algorithm runs on.
kpeter@814:     /// \param lower The lower bounds of the arcs.
kpeter@814:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@814:     /// \param cost The cost (length) values of the arcs.
kpeter@814:     /// \param supply The supply values of the nodes (signed).
kpeter@814:     CycleCanceling( const Digraph &digraph,
kpeter@814:                     const LowerMap &lower,
kpeter@814:                     const CapacityMap &capacity,
kpeter@814:                     const CostMap &cost,
kpeter@814:                     const SupplyMap &supply ) :
kpeter@814:       _graph(digraph), _lower(&lower), _capacity(digraph), _cost(cost),
kpeter@814:       _supply(digraph), _flow(NULL), _local_flow(false),
kpeter@814:       _potential(NULL), _local_potential(false),
kpeter@814:       _res_graph(NULL), _res_cost(_cost)
kpeter@814:     {
kpeter@814:       // Check the sum of supply values
kpeter@814:       Supply sum = 0;
kpeter@814:       for (NodeIt n(_graph); n != INVALID; ++n) {
kpeter@814:         _supply[n] = supply[n];
kpeter@814:         sum += _supply[n];
kpeter@814:       }
kpeter@814:       _valid_supply = sum == 0;
kpeter@814: 
kpeter@814:       // Remove non-zero lower bounds
kpeter@814:       for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@814:         _capacity[e] = capacity[e];
kpeter@814:         if (lower[e] != 0) {
kpeter@814:           _capacity[e] -= lower[e];
kpeter@814:           _supply[_graph.source(e)] -= lower[e];
kpeter@814:           _supply[_graph.target(e)] += lower[e];
kpeter@814:         }
kpeter@814:       }
kpeter@814:     }
kpeter@814: /*
kpeter@814:     /// \brief General constructor (without lower bounds).
kpeter@814:     ///
kpeter@814:     /// General constructor (without lower bounds).
kpeter@814:     ///
kpeter@814:     /// \param digraph The digraph the algorithm runs on.
kpeter@814:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@814:     /// \param cost The cost (length) values of the arcs.
kpeter@814:     /// \param supply The supply values of the nodes (signed).
kpeter@814:     CycleCanceling( const Digraph &digraph,
kpeter@814:                     const CapacityMap &capacity,
kpeter@814:                     const CostMap &cost,
kpeter@814:                     const SupplyMap &supply ) :
kpeter@814:       _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
kpeter@814:       _supply(supply), _flow(NULL), _local_flow(false),
kpeter@814:       _potential(NULL), _local_potential(false), _res_graph(NULL),
kpeter@814:       _res_cost(_cost)
kpeter@814:     {
kpeter@814:       // Check the sum of supply values
kpeter@814:       Supply sum = 0;
kpeter@814:       for (NodeIt n(_graph); n != INVALID; ++n) sum += _supply[n];
kpeter@814:       _valid_supply = sum == 0;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Simple constructor (with lower bounds).
kpeter@814:     ///
kpeter@814:     /// Simple constructor (with lower bounds).
kpeter@814:     ///
kpeter@814:     /// \param digraph The digraph the algorithm runs on.
kpeter@814:     /// \param lower The lower bounds of the arcs.
kpeter@814:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@814:     /// \param cost The cost (length) values of the arcs.
kpeter@814:     /// \param s The source node.
kpeter@814:     /// \param t The target node.
kpeter@814:     /// \param flow_value The required amount of flow from node \c s
kpeter@814:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@814:     CycleCanceling( const Digraph &digraph,
kpeter@814:                     const LowerMap &lower,
kpeter@814:                     const CapacityMap &capacity,
kpeter@814:                     const CostMap &cost,
kpeter@814:                     Node s, Node t,
kpeter@814:                     Supply flow_value ) :
kpeter@814:       _graph(digraph), _lower(&lower), _capacity(capacity), _cost(cost),
kpeter@814:       _supply(digraph, 0), _flow(NULL), _local_flow(false),
kpeter@814:       _potential(NULL), _local_potential(false), _res_graph(NULL),
kpeter@814:       _res_cost(_cost)
kpeter@814:     {
kpeter@814:       // Remove non-zero lower bounds
kpeter@814:       _supply[s] =  flow_value;
kpeter@814:       _supply[t] = -flow_value;
kpeter@814:       for (ArcIt e(_graph); e != INVALID; ++e) {
kpeter@814:         if (lower[e] != 0) {
kpeter@814:           _capacity[e] -= lower[e];
kpeter@814:           _supply[_graph.source(e)] -= lower[e];
kpeter@814:           _supply[_graph.target(e)] += lower[e];
kpeter@814:         }
kpeter@814:       }
kpeter@814:       _valid_supply = true;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Simple constructor (without lower bounds).
kpeter@814:     ///
kpeter@814:     /// Simple constructor (without lower bounds).
kpeter@814:     ///
kpeter@814:     /// \param digraph The digraph the algorithm runs on.
kpeter@814:     /// \param capacity The capacities (upper bounds) of the arcs.
kpeter@814:     /// \param cost The cost (length) values of the arcs.
kpeter@814:     /// \param s The source node.
kpeter@814:     /// \param t The target node.
kpeter@814:     /// \param flow_value The required amount of flow from node \c s
kpeter@814:     /// to node \c t (i.e. the supply of \c s and the demand of \c t).
kpeter@814:     CycleCanceling( const Digraph &digraph,
kpeter@814:                     const CapacityMap &capacity,
kpeter@814:                     const CostMap &cost,
kpeter@814:                     Node s, Node t,
kpeter@814:                     Supply flow_value ) :
kpeter@814:       _graph(digraph), _lower(NULL), _capacity(capacity), _cost(cost),
kpeter@814:       _supply(digraph, 0), _flow(NULL), _local_flow(false),
kpeter@814:       _potential(NULL), _local_potential(false), _res_graph(NULL),
kpeter@814:       _res_cost(_cost)
kpeter@814:     {
kpeter@814:       _supply[s] =  flow_value;
kpeter@814:       _supply[t] = -flow_value;
kpeter@814:       _valid_supply = true;
kpeter@814:     }
kpeter@814: */
kpeter@814:     /// Destructor.
kpeter@814:     ~CycleCanceling() {
kpeter@814:       if (_local_flow) delete _flow;
kpeter@814:       if (_local_potential) delete _potential;
kpeter@814:       delete _res_graph;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Set the flow map.
kpeter@814:     ///
kpeter@814:     /// Set the flow map.
kpeter@814:     ///
kpeter@814:     /// \return \c (*this)
kpeter@814:     CycleCanceling& flowMap(FlowMap &map) {
kpeter@814:       if (_local_flow) {
kpeter@814:         delete _flow;
kpeter@814:         _local_flow = false;
kpeter@814:       }
kpeter@814:       _flow = &map;
kpeter@814:       return *this;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Set the potential map.
kpeter@814:     ///
kpeter@814:     /// Set the potential map.
kpeter@814:     ///
kpeter@814:     /// \return \c (*this)
kpeter@814:     CycleCanceling& potentialMap(PotentialMap &map) {
kpeter@814:       if (_local_potential) {
kpeter@814:         delete _potential;
kpeter@814:         _local_potential = false;
kpeter@814:       }
kpeter@814:       _potential = &map;
kpeter@814:       return *this;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \name Execution control
kpeter@814: 
kpeter@814:     /// @{
kpeter@814: 
kpeter@814:     /// \brief Run the algorithm.
kpeter@814:     ///
kpeter@814:     /// Run the algorithm.
kpeter@814:     ///
kpeter@814:     /// \param min_mean_cc Set this parameter to \c true to run the
kpeter@814:     /// "Minimum Mean Cycle-Canceling" algorithm, which is strongly
kpeter@814:     /// polynomial, but rather slower in practice.
kpeter@814:     ///
kpeter@814:     /// \return \c true if a feasible flow can be found.
kpeter@814:     bool run(bool min_mean_cc = false) {
kpeter@814:       return init() && start(min_mean_cc);
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// @}
kpeter@814: 
kpeter@814:     /// \name Query Functions
kpeter@814:     /// The result of the algorithm can be obtained using these
kpeter@814:     /// functions.\n
kpeter@814:     /// \ref lemon::CycleCanceling::run() "run()" must be called before
kpeter@814:     /// using them.
kpeter@814: 
kpeter@814:     /// @{
kpeter@814: 
kpeter@814:     /// \brief Return a const reference to the arc map storing the
kpeter@814:     /// found flow.
kpeter@814:     ///
kpeter@814:     /// Return a const reference to the arc map storing the found flow.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@814:     const FlowMap& flowMap() const {
kpeter@814:       return *_flow;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Return a const reference to the node map storing the
kpeter@814:     /// found potentials (the dual solution).
kpeter@814:     ///
kpeter@814:     /// Return a const reference to the node map storing the found
kpeter@814:     /// potentials (the dual solution).
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@814:     const PotentialMap& potentialMap() const {
kpeter@814:       return *_potential;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Return the flow on the given arc.
kpeter@814:     ///
kpeter@814:     /// Return the flow on the given arc.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@814:     Capacity flow(const Arc& arc) const {
kpeter@814:       return (*_flow)[arc];
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Return the potential of the given node.
kpeter@814:     ///
kpeter@814:     /// Return the potential of the given node.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@814:     Cost potential(const Node& node) const {
kpeter@814:       return (*_potential)[node];
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Return the total cost of the found flow.
kpeter@814:     ///
kpeter@814:     /// Return the total cost of the found flow. The complexity of the
kpeter@814:     /// function is \f$ O(e) \f$.
kpeter@814:     ///
kpeter@814:     /// \pre \ref run() must be called before using this function.
kpeter@814:     Cost totalCost() const {
kpeter@814:       Cost c = 0;
kpeter@814:       for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@814:         c += (*_flow)[e] * _cost[e];
kpeter@814:       return c;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// @}
kpeter@814: 
kpeter@814:   private:
kpeter@814: 
kpeter@814:     /// Initialize the algorithm.
kpeter@814:     bool init() {
kpeter@814:       if (!_valid_supply) return false;
kpeter@814: 
kpeter@814:       // Initializing flow and potential maps
kpeter@814:       if (!_flow) {
kpeter@814:         _flow = new FlowMap(_graph);
kpeter@814:         _local_flow = true;
kpeter@814:       }
kpeter@814:       if (!_potential) {
kpeter@814:         _potential = new PotentialMap(_graph);
kpeter@814:         _local_potential = true;
kpeter@814:       }
kpeter@814: 
kpeter@814:       _res_graph = new ResDigraph(_graph, _capacity, *_flow);
kpeter@814: 
kpeter@814:       // Finding a feasible flow using Circulation
kpeter@814:       Circulation< Digraph, ConstMap<Arc, Capacity>, CapacityArcMap,
kpeter@814:                    SupplyMap >
kpeter@814:         circulation( _graph, constMap<Arc>(Capacity(0)), _capacity,
kpeter@814:                      _supply );
kpeter@814:       return circulation.flowMap(*_flow).run();
kpeter@814:     }
kpeter@814: 
kpeter@814:     bool start(bool min_mean_cc) {
kpeter@814:       if (min_mean_cc)
kpeter@814:         startMinMean();
kpeter@814:       else
kpeter@814:         start();
kpeter@814: 
kpeter@814:       // Handling non-zero lower bounds
kpeter@814:       if (_lower) {
kpeter@814:         for (ArcIt e(_graph); e != INVALID; ++e)
kpeter@814:           (*_flow)[e] += (*_lower)[e];
kpeter@814:       }
kpeter@814:       return true;
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Execute the algorithm using \ref BellmanFord.
kpeter@814:     ///
kpeter@814:     /// Execute the algorithm using the \ref BellmanFord
kpeter@814:     /// "Bellman-Ford" algorithm for negative cycle detection with
kpeter@814:     /// successively larger limit for the number of iterations.
kpeter@814:     void start() {
kpeter@814:       typename BellmanFord<ResDigraph, ResidualCostMap>::PredMap pred(*_res_graph);
kpeter@814:       typename ResDigraph::template NodeMap<int> visited(*_res_graph);
kpeter@814:       std::vector<ResArc> cycle;
kpeter@814:       int node_num = countNodes(_graph);
kpeter@814: 
kpeter@814:       int length_bound = BF_FIRST_LIMIT;
kpeter@814:       bool optimal = false;
kpeter@814:       while (!optimal) {
kpeter@814:         BellmanFord<ResDigraph, ResidualCostMap> bf(*_res_graph, _res_cost);
kpeter@814:         bf.predMap(pred);
kpeter@814:         bf.init(0);
kpeter@814:         int iter_num = 0;
kpeter@814:         bool cycle_found = false;
kpeter@814:         while (!cycle_found) {
kpeter@814:           int curr_iter_num = iter_num + length_bound <= node_num ?
kpeter@814:                               length_bound : node_num - iter_num;
kpeter@814:           iter_num += curr_iter_num;
kpeter@814:           int real_iter_num = curr_iter_num;
kpeter@814:           for (int i = 0; i < curr_iter_num; ++i) {
kpeter@814:             if (bf.processNextWeakRound()) {
kpeter@814:               real_iter_num = i;
kpeter@814:               break;
kpeter@814:             }
kpeter@814:           }
kpeter@814:           if (real_iter_num < curr_iter_num) {
kpeter@814:             // Optimal flow is found
kpeter@814:             optimal = true;
kpeter@814:             // Setting node potentials
kpeter@814:             for (NodeIt n(_graph); n != INVALID; ++n)
kpeter@814:               (*_potential)[n] = bf.dist(n);
kpeter@814:             break;
kpeter@814:           } else {
kpeter@814:             // Searching for node disjoint negative cycles
kpeter@814:             for (ResNodeIt n(*_res_graph); n != INVALID; ++n)
kpeter@814:               visited[n] = 0;
kpeter@814:             int id = 0;
kpeter@814:             for (ResNodeIt n(*_res_graph); n != INVALID; ++n) {
kpeter@814:               if (visited[n] > 0) continue;
kpeter@814:               visited[n] = ++id;
kpeter@814:               ResNode u = pred[n] == INVALID ?
kpeter@814:                           INVALID : _res_graph->source(pred[n]);
kpeter@814:               while (u != INVALID && visited[u] == 0) {
kpeter@814:                 visited[u] = id;
kpeter@814:                 u = pred[u] == INVALID ?
kpeter@814:                     INVALID : _res_graph->source(pred[u]);
kpeter@814:               }
kpeter@814:               if (u != INVALID && visited[u] == id) {
kpeter@814:                 // Finding the negative cycle
kpeter@814:                 cycle_found = true;
kpeter@814:                 cycle.clear();
kpeter@814:                 ResArc e = pred[u];
kpeter@814:                 cycle.push_back(e);
kpeter@814:                 Capacity d = _res_graph->residualCapacity(e);
kpeter@814:                 while (_res_graph->source(e) != u) {
kpeter@814:                   cycle.push_back(e = pred[_res_graph->source(e)]);
kpeter@814:                   if (_res_graph->residualCapacity(e) < d)
kpeter@814:                     d = _res_graph->residualCapacity(e);
kpeter@814:                 }
kpeter@814: 
kpeter@814:                 // Augmenting along the cycle
kpeter@814:                 for (int i = 0; i < int(cycle.size()); ++i)
kpeter@814:                   _res_graph->augment(cycle[i], d);
kpeter@814:               }
kpeter@814:             }
kpeter@814:           }
kpeter@814: 
kpeter@814:           if (!cycle_found)
kpeter@814:             length_bound = length_bound * BF_LIMIT_FACTOR / 100;
kpeter@814:         }
kpeter@814:       }
kpeter@814:     }
kpeter@814: 
kpeter@814:     /// \brief Execute the algorithm using \ref Howard.
kpeter@814:     ///
kpeter@814:     /// Execute the algorithm using \ref Howard for negative
kpeter@814:     /// cycle detection.
kpeter@814:     void startMinMean() {
kpeter@814:       typedef Path<ResDigraph> ResPath;
kpeter@814:       Howard<ResDigraph, ResidualCostMap> mmc(*_res_graph, _res_cost);
kpeter@814:       ResPath cycle;
kpeter@814: 
kpeter@814:       mmc.cycle(cycle);
kpeter@814:       if (mmc.findMinMean()) {
kpeter@814:         while (mmc.cycleLength() < 0) {
kpeter@814:           // Finding the cycle
kpeter@814:           mmc.findCycle();
kpeter@814: 
kpeter@814:           // Finding the largest flow amount that can be augmented
kpeter@814:           // along the cycle
kpeter@814:           Capacity delta = 0;
kpeter@814:           for (typename ResPath::ArcIt e(cycle); e != INVALID; ++e) {
kpeter@814:             if (delta == 0 || _res_graph->residualCapacity(e) < delta)
kpeter@814:               delta = _res_graph->residualCapacity(e);
kpeter@814:           }
kpeter@814: 
kpeter@814:           // Augmenting along the cycle
kpeter@814:           for (typename ResPath::ArcIt e(cycle); e != INVALID; ++e)
kpeter@814:             _res_graph->augment(e, delta);
kpeter@814: 
kpeter@814:           // Finding the minimum cycle mean for the modified residual
kpeter@814:           // digraph
kpeter@814:           if (!mmc.findMinMean()) break;
kpeter@814:         }
kpeter@814:       }
kpeter@814: 
kpeter@814:       // Computing node potentials
kpeter@814:       BellmanFord<ResDigraph, ResidualCostMap> bf(*_res_graph, _res_cost);
kpeter@814:       bf.init(0); bf.start();
kpeter@814:       for (NodeIt n(_graph); n != INVALID; ++n)
kpeter@814:         (*_potential)[n] = bf.dist(n);
kpeter@814:     }
kpeter@814: 
kpeter@814:   }; //class CycleCanceling
kpeter@814: 
kpeter@814:   ///@}
kpeter@814: 
kpeter@814: } //namespace lemon
kpeter@814: 
kpeter@814: #endif //LEMON_CYCLE_CANCELING_H